By the time Werner Heisenberg was in his 70s, there wasn’t much he didn’t know. He was a world-renowned theoretical physicist with a stash of prizes to his name, including a Nobel.

Yet, even as he lay on his deathbed in February of 1976, he longed to learn more.

“When I meet God, I am going to ask him two questions: why relativity? And why turbulence?” he reportedly quipped. “I really believe he will have an answer for the first.”

It’s a wonderful line to go out on – not least because, to the layperson at least, it’s rather unexpected. After all, it’s rare to see relativity come out as the easier option against… well, anything really, let alone a phenomenon you last heard about when an airplane trip got a bit rocky.

But nearly half a century later, we’re still struggling to understand turbulence. So what is the phenomenon all about? What makes it so bewildering? And more to the point – what makes it so endlessly fascinating?

**What is turbulence?**

There are really two answers to the question “what is turbulence?” Or, possibly, none. It depends on how you look at it.

“We don’t actually have a universally agreed-upon definition for turbulence in the science community,” James Beattie, a PhD Student in theoretical physics at the Australian National University, told IFLScience.

“It’s one of those things that ‘you know it when you see it’, so to speak.”

Take a step back, and we all know what turbulence is. Assuming you take milk in your coffee, you’ll have seen the clouds of white blossoming up and spreading throughout the drink, making intricate swirls in the liquid before eventually settling down into a perfectly blended cup of java.

That’s turbulence. It’s what you get when a fluid is moving as a collection of eddies – tiny whirlpools and the reverse current they create – constantly changing their size, speed, and orientation as they interact with and influence each other. It is, essentially, the way the universe mixes itself.

“Turbulence is chaos – unpredictable, rapidly-changing flow,” Blair Johnson, Assistant Professor in the Johnson Environmental Turbulence (JET) Laboratory at the University of Texas at Austin, told IFLScience.

“It is why boats have wakes and why volcanic ash clouds spread into the atmosphere, [mixing with] their surroundings.”

But dig a little deeper, and things start to get way muddier – and far more mind-bending.

“Turbulence is a type of fluid instability,” begins Beattie. Then: “What do I mean by ‘instability’? I mean that if I was to disturb (think a gentle prod) a fluid in a turbulent state, that disturbance would grow everywhere in space, and in time (exponentially fast!!!).”

Imagine sticking a twig into a muddy puddle: all that silt and dirt swooshing around in the rainwater reacts to the intrusion by creating those psychedelic-looking swirls around it. But aren’t we begging the question a little here? By defining turbulence as something that happens when a fluid is turbulent, are we really any closer to an explanation?

“Okay, but what makes the fluid go into the turbulent state to begin with?” Beattie says. “This brings us to what kind of fluid instability turbulence is: turbulence is a so-called high-Reynolds number instability.”

The Reynolds number in a fluid is calculated by taking the ratio of the fluid’s inertial force – the force coming from the momentum of the flow – and its viscous forces – how “gloopy” it is, basically.

If the inertial force is much bigger than the viscous force, you’re dealing with a fluid that’s got a lot of momentum behind it and low viscosity – a high Reynolds number flow. The opposite case, where the inertial force is low and the viscous force is high, would have a low Reynolds number.

Think running a bath (high Reynolds number) versus carefully pouring honey into a bowl (low Reynolds number). At some point on this honey-to-bathwater scale, the fluid dynamics change from being calm (or laminar) to turbulent.

One of the clearest demonstrations of this came from Reynolds himself. In a now-classic experiment, he introduced dye into the center of a clear pipe filled with flowing water. When the water had a low velocity, and therefore lower inertial force, the dye stayed as a distinct visible layer throughout the pipe. As the velocity of the water was increased, however, turbulence kicked in, and the two liquids mixed together.

The transition happens when we have a high Reynolds number: “when the forces associated with moving the fluid around are much larger than the forces responsible for dissipating the energy,” Beattie explains. Textbooks will often give rough figures for Reynolds numbers classifications: less than 2,000, and the flow is laminar, for example; more than 4,000, and it’s turbulent.

But for individual cases, Beattie says, “we don’t necessarily know how large is large enough.”

“As far as I know, understanding in detail the exact Re [Reynolds number] transition for many different fluid systems is still an open question in turbulence theory,” he adds, “so already you see that we don’t even know when the onset of turbulence begins!”

**Turbulence: too complex for God?**

We live in an age of robot guard dogs and anatomically accurate metaverse mammoths. How is it that so much about turbulence – a topic in a branch of physics and math that’s been around for two centuries already – is still unknown?

“Turbulence is described by Newton's second law of motion: force equals mass times acceleration,” Paul Williams, Professor of Atmospheric Science at the University of Reading, told IFLScience.

“Sounds nice and simple, right? But the difficulty arises because acceleration is most naturally expressed in a coordinate system that moves with the fluid, whereas the forces are most naturally expressed in a coordinate system that is fixed in space,” he explains.

While it’s possible to translate between these two coordinate systems, doing so leaves us with an extra – and nonlinear – term in the equation. That’s what gives us turbulence – it’s basically a wildcard addition to the system, explains Beattie: “You can think of [it] like climate versus weather.”

“Any turbulent quantity, like density, pressure, velocity, momentum, etc. can be decomposed in a mean-field and fluctuating component,” he says. “For the weather, the temperature fluctuates (fluctuating component) around the mean-field (climate), more or less.”

Turbulence is a stochastic process, Beattie points out, making it unpredictable by nature – randomness is stochasticity’s defining feature. In real-world experiments, that intrinsic randomness is compounded by all sorts of practical issues.

“My lab experiments, for example, take place in a cube less than 1 cubic meter [35 cubic feet], where 256 independently-firing jets generate turbulence in water,” says Johnson. “Every time I turn the jets on, I'm going to see ever-so-slightly different behavior – maybe the water temperature is a little warmer today, or the jets got bumped by a millimeter, or maybe the water was still moving a little bit from the experiments the day before.”

They may seem like little things – but little things make a big difference when chaos enters the equation. This is the field that brought us the butterfly effect, after all.

It’s just that when you’re trying to predict turbulence, you don’t even know how hard the little guy is flapping.

“We never know our boundary conditions with 100 percent certainty, and when you add chaotic forcing (wind, fish, flexible vegetation) on top of that, there's always going to be something you can't fully predict,” says Johnson. “I'm picturing a pre-school classroom where all of the kids just had their first dose of caffeine – can you predict what's going to happen?”

Still, you kind of get the feeling that’s part of the fun.

“Without turbulence, we would live in a very boring Universe,” says Beattie.

**Chaos at every scale**

As a rule, the natural world loves weird math. Some of the most stable and familiar patterns around us – florets on a cauliflower, for example – owe their trademark structures to the kind of math that lets you prove a triangle can exist in 1.6 dimensions.

That’s right: we’re talking about fractals.

“One of the most fascinating parts of science is how one can explain so many things as the same thing, happening on different scales in the Universe,” says Beattie. “Turbulence ends up being ‘that’ thing in the Universe – it is absolutely ubiquitous in across many of the scales of the Universe, both in space and in time.”

Turbulence, in its purest form, is fractal on a near incomprehensible scale. “As Re gets larger and larger the ‘length scales’ in the fluid that are responsible for dissipating energy are becoming separated from the scales that are moving the energy around in the fluid,” Beattie explains. “Mathematically, the energy in the fluid starts to follow a fractal structure.”

Take the Reynolds number to an extreme – let it “tend to infinity,” as mathematicians would say – and we start to approach a situation where a fluid’s inertia is so much larger than its viscosity that, for all intents and purposes, there is no viscosity at all. And we can imagine exactly when these circumstances would turn up: in the flow of a cloud of plasma moving through space.

“In astrophysics, turbulence is very hard to not run into,” says Beattie.

“It is responsible for the twinkling of stars […] and is a key process in regulating the star formation cycle in the modern Universe, making the whole process incredibly inefficient,” he explains. “[And] it is most likely responsible for growing and maintaining magnetic fields (the so-called small-scale turbulent dynamo) in the interstellar medium of galaxies.”

**A turbulent future**

Will turbulence ever be tamed?

With the advent of supercomputers and advanced numerical modeling, we’re getting a better understanding of the phenomenon all the time: “we have a solid understanding of how turbulence is 'supposed' to behave in a statistical sense,” says Johnson. “We can measure flow properties and characterize the energy with relative ease, and we have wonderful names for many of the instabilities that instantaneously contribute to mixing.”

But if we want to get much further, there are a couple of hurdles in our way.

“One of the Millennium prize problems […] is about the existence and smoothness of solutions to the Navier-Stokes equations – the same ones that ought to govern our turbulent flows,” says Beattie. “Understanding these equations […] more or less has to be the first step in understanding turbulence.”

“Well, for arbitrary initial conditions to the equations, which could a turbulent plasma configuration, mathematicians can’t even guarantee that a solution exists, and that it is well-behaved.”

That’s a problem because the world – and how we exist within it – is set to get a lot more turbulent in the future.

“Academically, turbulence courses are typically hosted in Mechanical & Aerospace Engineering departments,” says Johnson. “But we're starting to apply turbulence in many other areas now, such as predicting glacier melting and impacts of climate change, or looking at bio-inspired design for wind energy.”

“We know that climate change is making the atmosphere more turbulent. Our published projections indicate perhaps three times as much severe turbulence on busy midlatitude flight routes in the coming decades,” adds Williams. “The clock is ticking, but we are working on it.”

**Celebrating Chaos**

It’s been five hundred years since Leonardo Da Vinci first recorded – in his trademark backward, cipher-like scrawl – the “two motions” that characterize turbulence. Since then, it’s cropped up all over the place: in the swirling skies of Van Gogh’s *Starry Night*; in the images of Jupiter sent down to us from Juno; even in the lyrics of a rap song.

“There's a poem by Lewis Fry Richardson from 1922,” says Johnson. “*Big whorls have little whorls, Which feed on their velocity, And little whorls have lesser whorls, And so on to viscosity*.”

“The poem is read on day one of almost all graduate Turbulence courses,” she says. “This poem also makes an appearance in a Lupe Fiasco piece – *Dots & Lines*. I'd love to know how the turbulence poem infiltrated the rap community.”

“Or maybe, how turbulence *entrained* the rap world,” she jokes.

Despite its ability to frustrate us in the classroom, we have to give turbulence its dues. After all, life wouldn’t be the same without it.

“Breaking waves, forest fires, coastal protection with mangroves, shaking up your facial cleanser to mix the oil and water – turbulence is everywhere,” explains Johnson.

“Turbulence is what lets us survive,” she adds. “Without it, we'd be inhaling our own carbon dioxide, but instead, turbulence brings us fresh air.”

*All “explainer” articles are confirmed by fact checkers to be correct at time of publishing. Text, images, and links may be edited, removed, or added to at a later date to keep information current.*